In plays,
poems, and drama of the classical period, Greco-Roman deities
often had epithets attached
to their names. These epithets could serve either a ritualistic
function or a literary one.

In terms of
ritual, anthropologists note how hymns and chants to deities
might specify which deity is being
called upon. For instance, a Greek or Roman worshiper
might want to specify the Cytherian Venus (the
one born on the
isle
of Cyprus)
or the Egyptian equivalent (Bast, the foreign equivalent),
and they didn't want any confusion about which version
or manifestation of the deity should respond. Since the
Greco-Roman pantheon had no sacred
text to "standardize" belief about the appearance,
location, and personality of the gods, the worshiper
could avoid
such confusion by this specificity. Likewise, an epithet
could be used to specify a particular skill or role associated
with that deity. If a traveler wants Zeus to protect
him, it would be wise
to pray to Zeus Xenios (Zeus, the protector of
guests and overseer of hospitality) rather than Zeus
Ombrios (Zeus,
the bringer of storm-clouds). After all, the worshiper
wants to be looked after; he doesn't want to be rained
on!

In terms
of poetry,
these
epithets also served a poetic function. Poets like the
Homer or Sappho could use standard stock-descriptions
during spontaneous
performance to flesh out a line if they forgot some bit
as they recited a verse, or use them as mnemonic bridges
to
the next section of the poem. Additionally, when trying
to create verse like dactylic hexameter, poets would
use epithets because they served as appealing "filler"
to
complete the last few necessary syllables in a line.
Often, the Greek
or Roman epithets were perfectly suitable for inserting
in either a three-syllable or six syllable section of
poetry, so a single hexameter or two hexameters were
always available
in the poetic toolbox. Here are some common epithets
I've taken from Walter Burkert's Greek Religion (Cambridge,
2003):

Epithets
for Aphrodite:Aphrodite
Urania--Aphrodite the heavenly
Aphrodite the Golden
Aphrodite Kypris--The Aphrodite of Cyprus, the Cytherian
Venus
Aphrodite Paphos--The Aphrodite of Paphos
Aphrodite, Mother of the Mountain (Burkert 154)
Aphrodite, Daughter of Zeus (This epithet only appears in certain epics;
contrast with Hesiod in which Aphrodite is born from
sea-foam)
Aphrodite Philommeides--Laughter-loving Aphrodite
Aphrodite Pandemos--Aphrodite, lover of the whole people
[partly in the specific sense of Aphrodite being a goddess
of prostitution, but also in the sense of an all-embracing
love of people
as a whole]
Aphrodite Polos--Aphrodite, the high-crowned
Venus Genetrix--Venus the progenitor [a Roman cult made
popular by the Aeneas tradition and Julius Caesar]
Aphrodite Areia--Warlike Aphrodite
]

Epithets for Apollo:Apollo Epikourios--Apollo the Helper
(i.e., the Healer) (147)
Apollo Loxias--Apollo the Oblique (i.e., the one who gives confusing
oracles) (148)
Apollo Hekatebolos--Apollo, who strikes from afar (with his bow) (146)
Apollo Hekebolos--Apollo the afar, the distant one (146)
Apollo Hekatos--Apollo, who kills many (with plague) (146)
Apollo Delios--Delian Apollo, born on the island of Delos
Apollo Delphios--Delphian Apollo, protector of the shrine at Delphi
Apollo Despota--Apollo, the cruel master
Apollo Pythios--Pythian Apollo, slayer of the Python
Apollo Hyperboreos--Apollo, worshipped by the northmen
Apollo Mousagetes--Apollo, leader of the Nine Muses (147)
Apollo Daphnephorios--Apollo, carrier of the bay branches (147)
Apollo Apotropaios--Apollo, averter of evil (184)

Apollo's mottos as carved at the shrine of Delphi: "meden agan" [nothing
in excess] and "gnothi sauton" [know yourself]

In Cyprian Greek, the word for harvesting corn is damatrizein, which connects with the name Demeter or Damater. The Athenians called the dead Demetreioi and sowed corn on their graves.

Epithets for Dionysus:
Dionysus, son of Zeus
Dionysus Oinos--Dionysus the wine-god
Dionysus Polygethes--Dionysus, giver of many joys
Dionysus Orgios--Dionysus, the overseer of orgies
Dionyus Anthroporraistes--Dionysus, the destroyer of men, an epithet often written on tenedos (Burkert 164)
Dionysus Omestes--Dionysus, eater of raw flesh
Dionysus Lycurgus--Dionysus the wolf-repeller
Dionysus Bacchus--Dionysus the frenzied
Dionysus
Meilichios--Dionysus the mild

(Geographical tidbit: The volcanic Lipari Islands in Greek are the Hephaestiades insulae, and his smithy later located under Mount Etna in Roman literature).
Epithets for Hera:
Hera Zygia--Hera, protector of lawful
marriage (Burkert 184)
Hera Gamelios--Hera, protector of marriage rituals (184)
Hera Kourotrophos--Hera who nurses boys, an epithet she shares with Demeter (184)
Hera Teleia--Hera as watcher over the ultimate goal of marriage (184)
Hera is often listed as the ruling deity of Argos and (in Virgil) Carthage.

Epithets for Hermes/ Mercury:Hermes
Argeiphontes--Hermes, slayer of Argos (Burkert 157)
Hermes Psychopompos--Hermes, guide of the Dead (158)
Hermes Chthonias--Hermes, guide into the Underworld (158)
Hermes Phallos--Hermes the copulator (158)--a common one used by shepherds, and in legend, Hermes mastered his skills at seduction while living in the pastoral wilds.
Hermes Logos--Hermes, god of interpreters, fast-talk, and
good speech (158)
Hermes Agoraios--Hermes who brings profit in the market place (184) Hermaas Areias--Warlike Hermes--an epithet mostly confined to Mycenaean inscriptions (169)

In Greek, a
lucky find or an unexpected bout of good fortune is called
a hermaion.--i.e., a windfall from Hermes. Anyone skilled at or renowned for trickery was called a Hermides, "a son of Hermes." Thieves would also unabashedly pray to or call upon the name of Hermes as they stole something or to ask for help in their escape from wrathful pursuers. Hermes was also the god of interpreters, who were called hermeneus in Greek.

Originally, Tyche, "the lucky hit" appears to have been a personified abstraction turned into a deity after-the-fact in late Greece.

Epithets
for Zeus (Burkert 184): Zeus Xenios--Zeus,
the protector of guests
Zeus Ktêsios--Zeus, the guardian of possessions
in a house, protector of property.
Zeus Agoraios--Zeus, the lord of public assembly/
lord of the agora
Zeus Teleios--Zeus, the overseer of completion
in rituals (especially marriage)
Zeus Dikêphoros--Zeus, the harmonizer of
Olympian gods and spirits of the dead
Zeus Sóter--Zeus, the savior or "Third Saving
Zeus"
Zeus Panergetos--Zeus all-achieving
Zeus Olympios--Zeus, overseer of the Olympian
games
Zeus Ombrios--Zeus, the bringer of rain
Zeus Hyetios--Zeus, the bringer of storms
Zeus Herkeios--Zeus, the center of court
Zeus Polius--Zeus, the guardian of the city
Zeus Panhellenios--Zeus of all the Greeks
Zeus Agetor--Zeus as leader or commander
Zeus Diktaois--Zeus, keeper of the tenth month
Zeus the Shepherd of the Clouds
Zeus the Storm-gatherer
Zeus the Lightning-Wielder
Zeus Kronios--Chronian Zeus (i.e., Zeus, son of Chronos)
Zeus Kronides--Zeus, son of Chronos
Last of all, my personal favorite is "Zeus the Averter
of Flies," an epithet used by individuals attending the
Olympic and Delphic
games in Greece, who would buy small figurines of Zeus and
then
pray for him to smite dead the endless summer flies at these games.

Imagesof Gods:

Terminus was depicted simply as a large stone or boundary marker; he was not typically anthropomorphosized (Gibbon 1. Vol. , p 24)
Hermes at the port of Kyllene in Elis was worshipped in the shape of a phallos. His kerykeion, or herald's